Laser-based coordinate measuring device and laser-based method for measuring coordinates

ABSTRACT

A method for measuring a distance includes modulating the light beam at a first frequency, receiving a second beam by the optical detector to produce a first electrical signal having the first frequency and a first phase; modulating the light beam at a second frequency different than the first frequency; receiving the second beam by the optical detector to produce a second electrical signal having the second frequency and a second. After these steps, the retroreflector is moved while modulating the light beam continuously at the second frequency; and a first distance to the retroreflector is determined based at least in part on a the first and second frequencies and phases.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation application of U.S. Ser. No.14/685,076 filed Apr. 13, 2015 which is a Continuation application ofU.S. Ser. No. 13/287,513 filed Nov. 2, 2011 which is a Continuationapplication of U.S. Ser. No. 12/882,444 filed Sep. 15, 2010 now U.S.Pat. No. 8,120,780, which claims the benefit of U.S. patent applicationSer. No. 09/621,645 filed on Jul. 24, 2000 now U.S. Pat. No. 7,900,758.U.S. patent application Ser. No. 09/621,645 is a nonprovisionalapplication of U.S. Provisional Application No. 60/171,474 filed Dec.22, 1999, 60/145,686 filed Jul. 26, 1999 and 60/145,315 filed Jul. 23,1999, which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to a coordinate measuring device and, moreparticularly, to a laser based coordinate measuring device.

Discussion of the Related Art

There is a class of instrument that measures the coordinates of a pointby sending a laser beam to a retroreflector target that is in contactwith the point. The instrument determines coordinates by measuring thedistance and the two angles to the retroreflector target. There isanother class of instrument that is capable of measuring the threeorientation angles (pitch, yaw, and roll) of a retroreflector target. Ifsuch an instrument can also measure the three coordinates of a point inspace, it is said to measure six degrees of freedom. However, such sixdegree-of-freedom systems, whether or not they are employing lasertechniques, are generally inaccurate, slow, limited in radial or angularrange, and/or expensive. Exemplary systems for determining position(three to six degrees of freedom) are described by U.S. Pat. No.4,790,651 to Brown et al.; U.S. Pat. No. 4,714,339 to Lau et al.; U.S.Pat. No. 5,5059,789 to Salcudean; U.S. Pat. No. 5,367,373 toBusch-Vishniac et al.; U.S. Pat. No. 5,973,788 to Pettersen et al.; andU.S. Pat. No. 5,267,014 to Prenninger, et al. (the disclosures of whichare hereby incorporated by reference).

The laser tracker is a particular type of coordinate-measuring devicethat tracks the retroreflector target with one or more laser beams itemits. To provide a beam-steering mechanism for this tracking function,laser trackers conventionally include a stationary base onto which arotating stage or platform is mounted. Until now, most laser trackershave used optical elements, such as mirrors or prisms, to steer thelaser beam from its source in the base to optics in the rotating stageand through or off those optics toward the retroreflector. These opticalelements and their mounts are costly. Also, they are subject to tiltingand bending as a result of thermal and/or mechanical stresses that areusually present in tracker work environments. The consequence of thesestresses is reduced accuracy and stability. Examples of beam-steeringlaser trackers are described by Lucy, et al., Applied Optics, pp.517-524, 1966; Barnard and Fencil, Applied Optics, pp. 497-505, 1966;Sullivan, SPIE, Vol. 227, pp. 148-161, 1980; U.S. Pat. No. 4,020,340 toCooke; U.S. Pat. No. 4,025,193 to Pond; U.S. Pat. No. 4,386,848 toClendenin et al.; U.S. Pat. No. 4,436,417 to Hutchin; U.S. Pat. No.4,457,625 to Greenleaf et al.; U.S. Pat. No. 4,714,339 to Lau et al.;U.S. Pat. No. 4,721,385 to Jelalian et al.; Gennan Patent DE 3205362 A1to Pfeifer et al. (which are hereby incorporated by reference). Anexample of a beam-steering mechanism that uses prismatic opticalelements is described by U.S. Pat. No. 4,790,651 Brown et al. (which ishereby incorporated by reference).

A device that is closely related to a laser tracker is the laserscanner. The laser scanner steps one or more laser beams to points on adiffuse surface. The laser tracker and laser scanner are bothcoordinate-measuring devices. It is common practice today to use theterm laser tracker to also refer to laser scanner devices havingdistance- and angle-measuring capability. This broad definition of lasertracker, which includes laser scanners, is used throughout thisapplication.

An alternative to steering the laser beam with a mirror or prism is tolaunch the laser beam from an optical fiber mounted on a rigid platform.Although such devices have been built, none has taken full advantage ofthe simplicity, stability, and flexibility possible with such anapproach. For example, such systems usually require separate opticalfibers for transmitting and receiving the laser light. An exemplarysystem that tracks a laser beam launched from an optical fiber isdescribed in Nakarnura, et al., Review of Scientific Instruments, pp.1006-1011, 1994; Takatsuji et al., Measurement Science & Technology, pp.38-41, 1998; Takatsuji, et al., Measurement Science & Technology, pp.1357-1359, 1998; and Takatsuji, et al., Dimensional Metrology in the21^(st) Century, International Dimensional Metrology Workshop sponsoredby Oak Ridge Metrology Center, May 10-13, 1999 (which are herebyincorporated by reference). Non-tracking systems that launch laser beamsfrom optical fibers are numerous in the prior art and include U.S. Pat.No. 4,459,022 to Morey; U.S. Pat. No. 5,095,472 to Uchino, et al.; U.S.Pat. No. 5,198,874 to Bell et al.; U.S. Pat. No. 5,200,838 to Nudelman;U.S. Pat. No. 5,402,230 to Tian, et al.; U.S. Pat. No. 5,508,804 toFurstenau; and U.S. Pat. No. 5,557,406 to Taylor (which are herebyincorporated by reference).

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a laser-basedcoordinate measuring device that substantially obviates one or more ofthe problems due to limitations and disadvantages of the related art.

An object of the present invention is to provide a laser-basedcoordinate measuring device with improved laser beam steering, sixdegree of freedom measurements, and capability to locate multipleretroreflectors distributed throughout large volumes.

Another object of the present invention is to provide a reliablelaser-based coordinate measuring device that is easily manufactured at alow cost without complex beam-steering optics.

Additional features and advantages of the invention will be set forth inthe description that follows, and in part will be apparent from thedescription, or may be learned by practice of the invention. Theobjectives and other advantages of the invention will be realized andattained by the structure particularly pointed out in the writtendescription and claims hereof as well as the appended drawings.

To achieve these and other advantages and in accordance with the purposeof the present invention, as embodied and broadly described, a laserbased coordinate measuring device for measuring a position of a remotetarget comprising a stationary portion having at least a first laserradiation source and at least a first optical detector; a rotatableportion that is rotatable with respect to the stationary portion; and atleast a first optical fiber system for optically interconnecting thefirst laser radiation source and the first optical detector with anemission end of the first optical fiber system, the emission enddisposed on the rotatable portion for emitting laser radiation to theremote target and for receiving laser radiation reflected from theremote target, wherein an emission direction of the laser radiation iscontrolled according to the rotation of the rotatable portion.

In another aspect, a laser based coordinate measuring device comprises arigid structure rotatable about two substantially orthogonal axes; alaser radiation source disposed off the rigid structure to provide laserradiation; an optical detector disposed off the rigid structure; aretroreflective target disposed remote from the rigid structure; a firstoptical fiber path optically coupled with the laser radiation source totransmit laser radiation from the laser radiation source to the rigidstructure, the first optical fiber path having an end disposed on therigid structure for emitting the laser radiation to the retroreflectivetarget according to an orientation of the rigid structure and forreceiving retroreflected radiation reflected by the retroreflectivetarget; and an optical coupler optically connecting the optical detectorwith the first optical fiber path to receive the retroreflectedradiation.

In another aspect, a laser based coordinate measuring device formeasuring a position of a remote target comprises a stationary portionhaving at least a first laser radiation source; a rotatable portion thatis rotatable about first and second axes of rotation with respect to thestationary portion; an optical fiber path for optically interconnectingthe first laser radiation source with the rotatable portion, wherein afirst portion of the optical fiber path is disposed along the first axisand a second portion of the optical fiber path is disposed along thesecond axis.

In another aspect, a laser based coordinate measuring device comprises astructure rotatable about two substantially orthogonal axes; a laserradiation source disposed off the rotatable structure to provide laserradiation; a retroreflective target disposed remote from the rotatablestructure, the retroreflective target having a pattern thereon; anoptical system for directing the laser radiation from the laserradiation source to the rotatable structure and then to theretroreflective target in accordance with the rotation of the rotatablestructure, the retroreflective target reflecting the laser radiation tothe rotatable structure; and an orientation camera optically coupledwith the reflected laser radiation to determine an orientation of theretroreflective target, the orientation camera including a detector anda lens system that forms an image of the pattern on the detector.

In another aspect, a laser based coordinate measuring device comprises astructure rotatable about two substantially orthogonal axes; a laserradiation source disposed off the rotatable structure to provide laserradiation; a retroreflective target disposed remote from the rotatablestructure; an optical system for directing the laser radiation from thelaser radiation source to the rotatable structure and then to theretroreflective target in accordance with the rotation of the rotatablestructure, the retroreflective target reflecting the laser radiation tothe rotatable structure; and an orientation camera disposed on therotatable structure and optically coupled with the reflected laserradiation to determine a three dimensional orientation of theretroreflective target.

In another aspect, a laser based coordinate measuring system comprises astructure rotatable about two substantially orthogonal axes; a targetdisposed remote from the rotatable structure; a locator camera disposedon the rotatable structure for determining an approximate location ofthe target; and an actuator system to orient the rotatable structure inaccordance with the location determined by the locator camera.

In another aspect, a laser based method for measuring coordinates of aremote retroreflective target comprises the steps of coupling laserradiation into a first end of an optical fiber path, the optical fiberpath having a second end disposed on a rotatable structure; controllingthe rotation of the rotatable structure to direct the laser radiation tothe remote retroreflective target; coupling a first portion ofretroreflected laser radiation with an orientation camera; coupling asecond portion of the retroreflected laser radiation with a distancemeter; and calculating three positional and three orientational degreesof freedom of the remote retroreflective target.

In another aspect, a distance measuring apparatus for measuring adistance from the apparatus to an object includes a first lens systemincluding at least one lens and a first source of light and a secondsource of light. In this aspect, the first light from the first sourceand a second light from the second source is transmitted toward theobject and the first light has a first wavelength and the second lighthas a second wavelength different from the first wavelength. A firstportion of the first light is reflected by the object and a secondportion of the second light is reflected by the object and the first andsecond portions pass through at least a portion of the first lenssystem. The apparatus also includes a first optical detector thatdetects the first portion and a second optical detector that detects thesecond portion and a first dichroic beam splitter and a second dichroicbeam splitter, each dichroic beam splitter adapted to reflect at leastone of the first light and the second light toward the first opticaldetector and the second optical detector, respectively.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and areintended to provide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constituteapart of this specification, illustrate embodiments of the invention. Inthe drawings:

FIG. 1 depicts an embodiment of a laser tracker according to the presentinvention with a beam-steering mechanism and six degree-of-freedommeasurement capability;

FIG. 2 depicts in block form the major components of a rigid structureof the laser tracker of FIG. 1;

FIG. 3 depicts in block form components of the beam combiner of FIG. 2;

FIG. 4 depicts the components of the coupler assembly of FIG. 3;

FIG. 5 depicts the components of the interferometer assembly of FIG. 3;

FIG. 6 depicts in block form components of the beam expander of FIG. 2;

FIG. 7 depicts in block form components of the orientation camera ofFIG. 2 showing the locations of the intermediate and final images;

FIGS. 8a and 8b define the coordinate system for an unrotatedcube-corner retroreflector;

FIGS. 9a and 9b show the effect of pitch angle on the retroreflector;

FIGS. 10a and 10b show the effect of yaw angle on the retroreflector;

FIGS. 11a and 11b show the effect of roll angle on the retroreflector;

FIG. 12 illustrates the appearance of the image on the photosensitivearray within the orientation camera;

FIG. 13 depicts the laser tracker of FIG. 1 where the rigid structure isrotated to enable a wide-field locator camera to simultaneously viewplural retroreflector targets;

FIG. 14a is a front view of the locator camera on the rigid structure;

FIG. 14b is a cross sectional view of the locator camera of FIG. 14ataken along line 14 b-14 b;

FIGS. 15a-15c depict the formation of an image on the wide-field locatorcamera;

FIG. 16 depicts a method of routing optical fibers near the twomechanical axes;

FIG. 17 depicts a probe assembly of the preferred second embodiment; and

FIG. 18 depicts a conventional laser tracker to which an orientationcamera has been added for measuring six degrees of freedom.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings.

The present invention may be implemented as a laser-based coordinatemeasurement machine, laser tracker, or other suitable system. Thepresent invention provides a new type of beam-steering mechanism; theability to measure six degrees of freedom rather than just three degreesof freedom; and the ability to locate a plurality of retroreflectortargets over a relatively wide field of view.

The invention does not require beam-steering optics because the laserlight is routed through the laser tracker with optical fibers ratherthan with beam-steering mirrors or prisms. Laser light is processed,detected, and analyzed by optical and electrical components located forthe most part away from the rotating elements within the tracker. Oneadvantage of this approach is that it reduces the size and cost of thelaser tracker system. Another advantage is that it improves accuracy andstability of the laser tracker system. The architecture is flexibleenough to allow any number of laser beams to be launched without the useof optical beam-steering components.

The invention also provides the laser tracker with the ability tomeasure the six degrees of freedom of a target object which, in anexemplary embodiment, may be a cube-corner retroreflector. Ahidden-point probe (capable of measuring points that are obscured fromview) can be formed by attaching the target object to one end of a shaftand a probe tip to the other end of the shaft. The target object mayalso be attached directly to a machine tool or to the end-effector of arobot to more precisely control the movement of the tool or robot.

The invention also provides the laser tracker with the ability todetermine the location of a plurality of retroreflector targets over arelatively large volume surrounding the tracker. To activate thetarget-locator feature of the tracker, the rotating portion of thetracker is turned to bring a ring of LED's surrounding a lens andphotosensitive array to face the retroreflector targets. Flashes oflight from the LED's travel to the retroreflectors then return to thetracker, where they pass through the lens onto the photosensitive array.The locations of the spots on the array indicate the angular directionsof the targets.

Because the invention has the capability of launching multiple laserbeams of different types, several modes of distance measurement arepossible. One mode of distance measurement uses a laser beam that tracksa retroreflector to indicate either absolute or incremental distance.Another mode of distance measurement uses a laser beam to scan a diffusesurface. Either or both modes of distance measurement may be included ina given coordinate-measuring device.

FIG. 1 shows a perspective, block-diagram view of a laser trackingsystem according to an embodiment of the invention. The laser trackingsystem comprises a laser tracker 100 and a probe assembly 180. The probeassembly comprises target object 185, adjustable stage 181, probe shaft170, and probe tip 171. The target object 185 comprises retroreflector107 and housing 109 comprise target object 185. Laser tracker 100 emitsa laser beam 153 toward cube-corner retroreflector 107 mounted onhousing 109. Housing 109 is attached to adjustable stage 181 that isdesigned to pivot about axis 182 and lock into place. Adjustable stage181 is attached to probe shaft 170, which is attached on the opposingend to probe tip 171. Probe tip 171 is held in contact with the object175 under evaluation. With the combination of laser tracker 100,computer 25, and probe assembly 180, it is possible to measure thecoordinates of the object 175 under evaluation, even if object 175 isnot directly accessible to the laser beam emitted from the tracker.

The configuration of the laser tracker of FIG. 1 will now be described.Laser 102 on stationary base 101 of the laser tracker 100 injects laserlight (at least essentially coherent light having one wavelength) into afirst end of an optical fiber 111. The laser of the absolute-distancemeter (ADM) 103 injects laser light into a first end of an optical fiber115 (as shown in FIG. 3) that is contained within optical fiber assembly112. Laser 104 injects laser light into a first end of an optical fiber110. These optical fibers are routed to rigid structure 190, at whichlocation laser light is launched out of the second end of optical fibers110, 111, 115 (as shown in FIG. 3). If desired, the combined laser lightmay be conditioned by optical elements within rigid structure 190 andemitted from rigid structure 190 as laser beam 153. Laser light 153travels to retroreflector 107, where it is reflected parallel to laserbeam 153. If laser beam 153 is centered on the vertex of the cube-cornerretroreflector, then laser beam 163 will coincide with laser beam 153.That is, laser beam 163 will retrace the path of laser beam 153. Thelaser beam 163 enters rigid structure 190, where it is conditioned, ifdesired, and injected back into optical fibers 110, 111, and/or 115, orotherwise detected and processed as explained below. Rigid structure 190is rotated by motor 81 with the angle of rotation indicated by angularencoder 91. Steering platform 195 includes rigid structure 190 and theelements mounted thereto, i.e., motor 81 and angular encoder 91.Steering platform 195 is turned on base 101 by motor 80, with the angleof rotation indicated by angular encoder 90. Rigid structure 190 istherefore supported for rotation about two orthogonal axes on base 101.

ADM 103 measures the absolute distance from laser tracker 100 toretroreflector 107. This device is capable of measuring the distance toretroreflector 107 in a single shot. Consequently, it can be used toperform rapid point-and-shoot measurements of multiple retroreflectortargets. Laser 104 is used in conjunction with optical and electricalelements to measure the incremental distance moved by retroreflector107. An example of a device that measures incremental-distance movementis the laser interferometer which measures the number of interferencefringes that occur as the retroreflector is moved from a startingposition. In a laser interferometer, if an obstruction is placed in thepath of the interferometer's laser beam, all displacement informationwill be lost. In this circumstance, if a laser-tracker system has onlyan incremental-distance measurement system and not an absolute-distancemeasurement system, then the retroreflector must be returned to areference position and the measurement started anew. Laser 102 is astand-alone laser and will be discussed in more detail with reference tofiber launch assembly 310 of FIG. 3. Any number of laser beams may besent over optical fibers into rigid structure 190.

Electronics box 140 provides electrical power to motors 80 and 81,angular encoders 90 and 91, lasers 102 and 104, ADM 103, as well asother electrical components within rigid structure 190. Electronics box140 analyzes signals from angular encoders 90 and 91, from ADM 103, andfrom other electrical components to calculate angles and distances fromtracker 100 to retroreflector 107. Electronics box 140 is attached tocomputer 25, which provides application software for the advancedanalysis of coordinate data.

The preferred optical elements within rigid structure 190 are shown inblock diagram form in FIG. 2. The main functional blocks within rigidstructure 190 include beam-combiner block 200, orientation-camera block210, beam-expander block 220, and locator-camera block 230.

The optical fiber assemblies 110, 111, 112, etc. are routed intobeam-combiner block 200, which combines the laser beams and sends themout as a single composite laser beam 250 that includes coherent light ata plurality of separate, discrete wavelengths. The composite laser beam250 passes through orientation-camera block 210 to become laser beam251. Laser beam 251 is beam expanded by beam-expander block 220, therebyexiting rigid structure 190 as expanded laser beam 153. The laser beam153 travels to retroreflector 107 as shown in FIG. 1 and returns aslaser beam 163. The laser beam 163 retraces the path of the outgoinglaser beams 153, 251, 250 back through beam-expander block 220 andorientation-camera block 210 into beam-combiner block 200. Electricallines 41 provide power from electronics box 140 to mechanical andelectro-optical devices. Electrical lines 41 also route electricalsignals from electro-optical devices to electronics box 140 foranalysis. Rigid structure 190 rotates around the center of shaft 270which is attached to motor 81 as shown in FIG. 1. In a typical mode ofoperation, motor 81 rotates rigid structure 190 so that laser beam 153points toward retroreflector 107, thereby causing laser beam 163 toretrace the path of laser beam 153. In another mode of operation, motor81 rotates rigid structure 190 until aperture 231 of locator camera 230is aimed in the general direction of one or more retroreflectors in thesurrounding environment. Locator camera 230 determines the approximatelocation of the retroreflector targets within a wide field of view.

Beam-Combiner Block

FIG. 3 shows diagrammatically the optical and electro-optical componentswithin a preferred beam-combiner block 200. The main assemblies withinbeam-combiner block 200 are first laser-beam fiber launch and pickupassembly 300, second laser-beam fiber launch and pickup assembly 320,laser-beam fiber launch assembly 310, and position-detector assembly340.

First laser-beam fiber launch and pickup assembly 300 receives light anend of optical fiber 115 which is attached at its opposing end to alaser in the laser and ADM 103 shown in FIG. 1. Laser light (at leastone essentially coherent light at a first discrete frequency) travels inoptical fiber 115 until it reaches coupler assembly 305. Part of thelaser light emerging from coupler assembly 305 is in optical fiber 306.It travels to fiber termination 301, at which point it diverges as coneof light 360. Lens 302 collimates this light as laser beam 361 whichpasses through beam splitter 314 to become laser beam 365. Another partof the laser light emerging from coupler assembly 305 travels through anoptical fiber 307 to fiber retroreflector 303 and returns throughoptical fiber 307 into coupler assembly 305 thereby forming a referencepath as will be discussed with reference to FIG. 4.

Laser-beam fiber launch assembly 310 receives light from an end ofoptical fiber 111 which is attached at its opposing end to laser 102shown in FIG. 1. Laser light travels in optical fiber 111 until itreaches fiber termination 311 where it diverges as cone of light 362.Lens 312 collimates the light as laser beam 363 which then reflects offmirror 313 to become laser beam 364. Laser beam 364 reflects off beamsplitter 314 to join laser beam 365 from first laser-beam fiber launchand pickup assembly 300. Laser beam 365 passes through beam splitter 324to become laser beam 369.

Second fiber launch and pickup assembly 320 receives light from an endof optical fiber 110 which is attached at its opposing end to laser 104shown in FIG. 1. Laser light travels in polarization-maintaining (PM)optical fiber 110 until it reaches fiber termination 321 where itdiverges as cone of light 366. Lens 322 collimates the laser light aslaser beam 370. Laser beam 370 passes into interferometer assembly 325and emerges as laser beam 367. The laser beam reflects off mirror 323 aslaser beam 368 and off beam splitter 324 as a part of laser beam 369.Laser beam 369 passes through beam splitter 342 to become laser beam250.

FIG. 2 shows that laser beam 250 passes out of beam-combiner block 200and continues through the rest of the elements in rigid structure 190,then travels as laser beam 153 to retroreflector 107 of FIG. 1 andreturns as laser beam 163 to rigid structure 190. The laser light ofbeam 163 retraces the path of laser beams 251, 250 through the opticalelements 220, 210 within rigid structure 190. As shown in FIG. 3, whenthe returning laser beam enters beam-combiner block 200, some of thereturning light reflects off beam splitter 342 as laser beam 374. Beamsplitter 342 reflects a portion of all of the wavelengths of laser lightwithin laser beam 250. Optical filter 343 blocks all but one wavelengthof the light within laser beam 374, which it transmits as laser beam373. Position detector 341 is aligned so that laser beam 373 strikes thecenter of position detector 341 when laser beam 153 of FIG. 1 iscentered on retroreflector 107. If laser beam 373 does not strike thecenter of position detector 341, an error signal is generated atdetector 341, thereby causing motors 80 and 81 to turn rigid structure190 to center laser beam 153 on retroreflector 107. In this way,position detector 341 enables the outgoing laser beam 153 of FIG. 1 toautomatically track a moving retroreflector 107. Position detector 341can be any device capable of giving an electrical signal in response tothe position of light on a two-dimensional surface. Such a device mayinclude, but is not limited to, a quadrant detector, a lateral-effectdetector, a charge-coupled-device (CCD) array, a charge-injection-device(CID) array, or a complementary-metal-oxide-semiconductor (CMOS) array.

The number of laser beams launched out of beam-combiner block 200 can beincreased or decreased as desired by adding more or fewer beam splitterswithin beam-combiner block 200. One way to combine and separatedifferent types of laser beams is on the basis of wavelength. A dichroicbeam splitter is a type of beam splitter that can pass particularwavelengths while reflecting other wavelengths. In a specificimplementation using dichroic beam splitters, optical fiber 115 may emitlaser light at a wavelength of 1550 nm, optical fiber 111 may emit laserlight at 690 nm, and optical fiber 110 may emit laser light at 633 nm.Thus, beam splitters 314 and 324 may be dichroic beam splitters with thefollowing characteristics. Beam splitter 314 transmits laser wavelengthslonger than 1400 nm, but reflects wavelengths shorter than 1400 nm. Beamsplitter 324 transmits wavelengths longer than 660 nm, but reflectswavelengths shorter than 660 nm. In this way, the laser beams arecombined as they pass through beam-combiner block 200 on the way out ofrigid structure 190. Similarly, the laser beams are separated on thereverse path through beam-combiner block 200. Combining and separatingthe wavelengths with dichroic beam splitters reduces the interactionamong the laser beams, thereby preventing measurement errors.Furthermore, the use of dichroic beam splitters reduces power loss thatwould result from the use of wavelength-insensitive beam splitters.

The laser beam sent out of fiber launch assembly 310 may serve a numberof purposes. In the specific example shown in FIGS. 1 and 3, the laserbeam launched from second laser-beam fiber launch and pickup assembly320 is red (633 nm), thereby providing a visible indication of thedirection to which the laser beam is pointing. In the event that thelaser beam from second laser-beam fiber launch and pickup assembly 320is turned off or, not visible, is otherwise not available, the laserbeam emitted by laser-beam fiber launch assembly 310 can serve as avisible pointer beam to assist the operator in locating retroreflectortargets with the tracker. This same laser beam may be used as a part ofa complex system for other purposes such as determining the orientationof a retroreflector target. There are occasions in which it is veryuseful to have the laser tracker emit multiple laser beams. As notedabove, the flexible architecture of the invention allows as few or asmany laser beams as desired to be launched.

FIG. 4 shows a detailed view of the coupler assembly 305. Laser lightenters coupler assembly 305 on optical fiber 115 and travels to Faradayisolator 420 which allows light to travel in only one direction. Faradayisolator 420 is included to prevent back-reflected laser light fromentering and destabilizing the laser found in the ADM 103. The laserlight passes through Faraday isolator 420 and enters optical coupler 401which, in an exemplary configuration, sends 85% of the optical power tooptical coupler 402 and 15% of the optical power to optical coupler 403.Of the optical power entering coupler 402, a portion such as one half issent to low-reflectance termination 412 and the remaining half travelsto optical fiber 306. As shown in FIGS. 1 and 3, the laser light inoptical fiber 306 is launched from the fiber and travels toretroreflector 107. The light from the retroreflector retraces its paththrough the laser tracker and re-enters optical fiber 306. When light isreceived via optical coupler 402, half of the optical power is sent tothe Faraday isolator 402 where it is blocked. The remainder is sent tooptical fiber 309 and continues to ADM 103 via optical fiber assembly112. Of the optical power that is sent from optical coupler 401 tooptical coupler 403, half travels to low-reflectance termination 413,and the other half travels along optical fiber 307 to fiberretroreflector 303. The light retraces its path back along optical fiber307 into coupler 403. Half of the optical power is sent to coupler 401where it is sent in equal parts to the low-reflectance termination 411and the Faraday isolator 420. The other half of the optical power issent into optical fiber 308 and continues to ADM 103 via optical fiberassembly 112.

The optical couplers shown in FIG. 4 split light into two paths in theforward direction and two paths in the reverse direction. Alow-reflectance termination is used to absorb the light in one of thefour possible paths (two forward paths plus two reverse paths). Anotherterm for a possible path is a “port,” so the couplers shown in FIG. 4are examples of four-port couplers having a low-reflectance terminationon one of the four ports. An alternative to the type of coupler shown inFIG. 4 is the optical circulator, which has three ports, rather thanfour, ports. In other words, in an optical circulator, the laser lighttravels along one optical-fiber path in the forward direction andbranches to a different optical fiber path in the reverse direction. Forthe purposes of this invention, the term optical coupler is used toencompass both four-port and three-port light splitting devices. Inother words, a term fiber-optic coupler (or simply coupler) isunderstood to include any type of device that splits light in an opticalfiber and therefore can be either a four-port coupler or a three-portcirculator.

For absolute-distance measurement, two paths are used: a measurementpath and a reference path. Both paths begin at the laser of the ADM 103and include the optical fiber 115 and the Faraday isolator 420. In themeasurement path, the laser light travels through optical fiber 306,through rigid structure 190, to the retroreflector 107 and back, intofibers 306 and 309, and then into a measurement detector (not shown) inthe ADM 103. In the reference path, the laser light travels throughoptical fiber 307, to the fiber retroreflector 303 and back, into fibers307 and 308, and then into a reference detector (not shown) in the ADM103. The optical fibers 308 and 309 are in the reference and measurementchannels, respectively, and are matched in length. They are routed inclose proximity to one another so that the local temperaturesexperienced by each are nearly equal. This commonality of length andtemperature has the effect of minimizing the errors caused bytemperature-induced changes in the index of refraction of the opticalfibers. Without this commonality, a changing temperature might bemistaken for a changing distance to the retroreflector.

Many types of ADM are compatible with the fiber delivery beam-steeringmechanism depicted in FIG. 1. While any suitable type of ADM can beemployed, an exemplary type of ADM operates by measuring the phase shiftof laser light that is intensity modulated by a sine wave. Thus, theparticular type of laser might be a distributed feedback (DFB)semiconductor laser whose optical power is modulated by the directapplication of a radio-frequency (RF) electrical signal at a single(sinusoidal) frequency of 3 GHz. For any given distance to theretroreflector 107, there will be a corresponding difference in thephase of the reference and measurement channels. If a is a constant, fis the frequency of modulation (3 GHz), c is the speed of light (≅3×10⁸m/s), n is the group index of refraction of the air through which thelaser light travels (≅1), m is an integer, and ϕ is the phase differencemeasured by the ADM, then the distance d from laser tracker 100 toretroreflector 107 is given by the following formula:

$\begin{matrix}{d = {a + {\frac{c}{2f\; n}{\left( {m + \frac{\phi}{2\pi}} \right).}}}} & (1)\end{matrix}$The constant a sets the distance scale so that a distance of zero is setat the pivot point through which the laser beam appears to emanate asthe laser tracker is turned to different angles. The pivot point islocated approximately at the intersection of the laser beam and thecenter of shaft 270. The integer m is equal to the number of completemultiples of 2π radians in the phase difference (measurement phase minusreference phase) measured by the ADM. For example, if the frequency ofmodulation f is 3 GHz, then from Eq. (1) the distance corresponding to aphase difference of 2π radians is approximately 3×10⁸/2(3×10⁹)(1) m=0.05m. This distance is sometimes referred to as the unambiguous range. Ifthe distance d−a is 1.22 meters, then the number of complete multiplesof 2π radians in the phase difference is int(1.22/0.05)=24 and theresidual phase shift is approximately ϕ≅2π(1.22−0.05.24)/0.05=0.8πradians. The most convenient way to determine the integer m is totemporarily reduce the frequency f to a value that is small enough tocover the entire range of interest, but with an accuracy that is largeenough to determine the value of m. For example, suppose that thefrequency is temporarily reduced to 2.5 MHz. In this case, theunambiguous range is 3×10⁸/2(2.5×10⁶)(1) m=60 m. If the accuracy of thephase measurement is one part in 10⁵, then the position ofretroreflector 107 is known to an accuracy of 60·10⁻⁵ m=0.6 mm at anydistance up to 60 meters from the tracker. This value is much smallerthan the unambiguous range of 50 mm for the higher modulation frequencyof 3 GHz. This means that a single measurement of phase difference withthe lower modulation frequency is sufficient to determine the integer min Eq. (1). This technique of reducing the frequency to determine thevalue of m is of greatest value if it is needed only at the start of ameasurement or after the laser beam has stopped tracking theretroreflector 107. For this to be the case, the phase measurements mustbe taken rapidly enough to ensure that the retroreflector has not movedover a complete unambiguous range between measurements. For example, ifmeasurements are made 1000 times per second, then the radial speed mustnot exceed (0.05)(1000)/2=25 meters per second. The human arm is notcapable of moving a retroreflector target at a radial speed of greaterthan about 4 meters per second, so this technique of determining m isfeasible under the conditions given above.

The modulated laser light that travels on optical fibers 308 and 309within optical fiber assembly 112 arrives at optical detectors locatedwithin ADM 103. These optical detectors convert the laser light toelectrical signals. For the particular type of ADM described above,electrical components within ADM 103 process the electrical signal todetermine the phase of the signal for the measurement and referencepaths.

As shown in FIG. 3, laser light that is launched from optical fiber 110is collimated by lens 322 to become laser beam 370. This laser beamtravels to interferometer assembly 325, a detailed view of which isshown in FIG. 5. The laser light of beam 370 is linearly polarized at 45degrees to the plane of the paper in FIG. 5. In other words, half of thelaser light is polarized in the plane of the paper and half of the lightis polarized perpendicular to the plane of the paper, with bothpolarizations having the same phase. The arrow that is perpendicular tolaser beam 370 in FIG. 5 represents the laser light that is polarized inthe plane. The small circle that is centered on laser beam 370 in FIG. 5represents the laser light that is polarized perpendicular to the planeof the paper. Laser beam 370 travels to polarizing beam splitter 501.The portion of laser beam 370 that is polarized perpendicular to theplane of the paper in FIG. 5 reflects off polarizing beam splitter 501to become laser beam 510. The light travels to quarter waveplate 502having a fast axis oriented at 45 degrees to the plane of the paper inFIG. 5. The waveplate converts the polarization state of laser beam 510from linear to circular. Lens 503 focuses the light onto mirror 504,which retroreflects the laser beam 510 back on itself. Alternatively, aretroreflector (such as a cube-corner retroreflector) may be substitutedfor lens 503 and mirror 504. Lens 503 collimates the retroreflectedlight, sending it back through quarter waveplate 502, changing thepolarization state of the light from circular to linear, with thedirection of the linearly polarized light now in the plane of the paper.This light, which is now p-polarized with respect to the polarizing beamsplitter 501, passes through the beam splitter to become part of laserbeam 511. That portion of laser beam 370 that is in the plane of thepaper in FIG. 5 travels straight through polarizing beam splitter 501 tobecome laser beam 367. This light passes through quarter waveplate 367,whose fast axis is oriented at 45 degrees with respect to the plane ofthe paper. When laser beam 367 passes through the waveplate, itspolarization state changes from linear to circular. The resulting laserbeam travels through the optical elements in rigid structure 190,travels to retroreflector 107, and travels back through the opticalelements in rigid structure 190 to arrive at quarter waveplate 505. Aslaser beam 367 travels in the reverse direction through quarterwaveplate 505, its polarization state changes from circular to linear,with the direction of the linearly polarized laser light now inperpendicular to the plane of the paper in FIG. 5. (As an alternative toplacing quarter waveplate 505 inside interferometer assembly 325, thewaveplate may be placed at some later point along the path of the laserbeam.) Laser beam 367, which is now s-polarized with respect topolarizing beam splitter 501, reflects off the beam splitter to becomepart of laser beam 511. Laser beam 511 comprises of two portions: areference portion that is polarized in the plane of the paper and ameasurement portion that is polarized perpendicular to the plane of thepaper. As the retroreflector 107 is moved in a radial direction withrespect to laser tracker 100, the phase difference between these twolinearly polarized components will vary. There will be a phase change of2π radians for each change of one-half wavelength in the radial distanceto the retroreflector. Here, the wavelength is that of the laser lightin laser beam 370 as seen in the local medium (air) through which thelaser light travels. Laser beam 511 travels to processing optics 506,which uses optical elements such as beamsplitters, waveplates, andoptical detectors to provide two electrical signals. One electricalsignal is proportional to cos p, and the other electrical signal isproportional to sin p, where p is the phase difference between the twolinearly polarized portions of laser beam 511. The electrical signalsare sent to a counter circuit 507 that counts the number of halfwavelengths traveled by retroreflector 107. The product of thewavelength of the light and the number of wavelengths traveled gives thetotal displacement of retroreflector 107 relative to some startingposition. Counter 507 sends electrical signals over electrical line 41to electronics box 140 for conversion from counts to a radial distance.If laser beam 153 is obstructed from reaching retroreflector 107, evenfor a moment, then information on the correct number of counts is lost,and the measurement must be started anew from some reference positionwhose distance to the tracker has been previously established. The typeof interferometer shown in FIG. 5 is known as a homodyne interferometerbecause the reference portion and measurement portion that are combinedto form laser beam 511 are both at the same wavelength. Alternatively, aheterodyne interferometer in which two different laser wavelengths aremixed together prior to optical detection or other suitable system couldbe used.

Beam-Expander Block

The optical components within beam-expander block 220 of FIG. 2 areshown in FIG. 6. The beam-expander block 220 expands the laser beam asit travels in the forward direction and to contract the laser beam as ittravels in the reverse direction. Lens 601 converts collimated laserbeam 251 into cone of light 651. Lens 602 converts cone of light 651into collimated laser beam 153.

The reason for expanding the laser beam before it leaves rigid structure190 is to reduce the divergence of the laser beam during propagation.This makes it possible to place retroreflector 107 farther from lasertracker 100 than would otherwise be the case. Alternatively, thebeam-expander block 220 could be eliminated by increasing the distancein FIG. 3 between the fiber terminations 301, 311, and 321 and thecorresponding lenses 302, 312, and 322 while increasing the focallengths of lenses 302,312, and 322 by a corresponding amount.Accordingly, the diameters of laser beams 361,363, and 370 would beincreased, thereby eliminating the need for beam-expander block 220. Thedisadvantage of this approach is that it requires that many opticalelements (lenses, mirrors, beam expanders, and position detector) bemade larger to accommodate the larger beam diameters. By addingbeam-expander block 220, the overall size of beam-combiner block 200 isreduced.

Orientation-Camera Block

The main elements of orientation-camera block 210 of FIG. 2 are shown inFIG. 7. On the return path from retroreflector 107, laser beam 251travels along optical axis 741. Beam splitter 701 reflects a portion ofthe beam to a path along optical-axis segments 750, 742, 743, and 744.Eventually, this reflected light arrives at photosensitive array 753.The complete lens system, which comprises the beam-expander block 220,afocal lens block 710, and relay lenses, 721 and 723, produces an imageon the photosensitive array of the pattern of light in the vicinity ofthe vertex of retroreflector 107. The beam-expander block 220 and theafocal lens block 710 work together to produce a first intermediateimage 751 of this pattern of light. The location of first intermediateimage 751 will depend on the distance of retroreflector 107 from thelaser tracker. Motorized stage 728 is activated to move lens 721 to anappropriate distance from first intermediate image 751. Lens 721 formssecond intermediate image 752 located past negative lens 723 but insidethe back focal point of negative lens 723. Negative lens 723 convertsthe second intermediate image into a real image 753 on photosensitivearray 725.

The orientation-camera block 210 allows the distance between the trackerand the retroreflector target to be large. For example, a distance ofmore than thirty meters is possible. The lens systems of theorientation-camera block 210 and beam-expander block 220 have two mainfunctions. First, a magnification that is approximately constant ismaintained so that the image will nearly fill the photosensitive array,thereby maintaining high accuracy for large and small distances alike.Second, the adverse effects of diffraction, which may result in lines orother features changing shape or direction during propagation over largedistances, are minimized. To maintain constant magnification, afocallens systems 220 and 710 are used. An afocal lens system is one thatconverts an incoming ray of light that is parallel to the optical axisinto an outgoing ray of light that is also parallel to the optical axis.A succession of afocal lens systems, as represented by the combinationof lens systems 220 and 710, has the property of constant magnification.In other words, the size of first intermediate image 751 is constant,regardless of the distance from retroreflector 107 to the tracker. Iffirst intermediate image 751 is located between lenses 711 and 714, thenit is not possible to place photosensitive array 725 at the location ofthis intermediate image. Relay lenses 721 and 723 eliminate this problemby converting first intermediate image 751 into image 753 on array 725.Motorized stage 728 places lens 721 an appropriate distance from firstintermediate image 751. Knowledge of the distance to retroreflector 107,which is a quantity measured by the tracker, along with knowledge of thefocal lengths and positions of the lens elements, is sufficient todetermine the correct placement of lens 721. As is explained below, itis not necessary for the lens system to obtain an exactly prescribedmagnification, so motorized stage 728 can be relatively inexpensive. Thedistance that motorized stage 728 must move will depend on the range ofdistances to be covered, as well as on the magnification of the lenssystem. Longitudinal magnification of a lens system varies in proportionto the square of the transverse magnification. As an example, supposethat a 12×12 millimeter area of target object 185 is imaged onto aphotosensitive array having an area of 3×3 mm. The required (transverse)magnification for the system will then be 3/12=¼. This could be achievedby making the combined magnification of the afocal lens systems equal to¼ and the combined magnification of the relay lenses 721 and 723 equalto 1. In this case, however, to cover distances of 1 to 33 meters fromthe tracker, it would be necessary for motorized stage 728 to have arange of movement of (33−1) m/4²=2 m. Such a large range of movement isimpractical for most real systems. To solve this problem, themagnification of the afocal lens systems could be reduced, and thereduced magnification could be compensated with the relay lenses. Forexample, suppose that the afocal lens pairs have a combinedmagnification of 1/32, while the relay lenses have a combinedmagnification of 8. In this case, the net magnification is still ¼, butthe motorized stage 728 needs to have a range of movement of only (33−1)m/32²=31.25 mm.

The photosensitive array 725 can be any device capable of returningdetailed electrical information about the pattern of light incident onthe array. Exemplary photosensitive arrays include thecharged-coupled-detector (CCD) array, the charge-injection-device (CID)array, and the complementary-metal-oxide-semiconductor (CMOS) array.Among these, CCD arrays have high performance and small size, but CMOSarrays are often capable of providing high-speed readout with simplerelectrical circuitry. CMOS and CID arrays often have the advantageousfeature of random-access readout of pixel data.

We will now discuss how the image on the orientation camera can be usedto determine the pitch, yaw, and roll angles of retroreflector 107.FIGS. 8a and 8b show an unrotated cube-corner retroreflector. In otherwords, in FIGS. 8a and 8b , the roll angle is zero, the yaw angle iszero, and the pitch angle is zero. By definition, the x direction shownin FIGS. 8a and 8b is opposite the direction of the laser beam that issent into the retroreflector. The three perpendicular reflectingsurfaces of the cube-corner retroreflector form three lines ofintersection. As shown in FIG. 8a , the x-y plane contains the x axisand one of the lines of intersection. The x-y plane also contains the yaxis, which is perpendicular to the x axis and passes through the vertexof the cube corner. The dashed line in FIG. 8a is parallel to the y axisand has been included for clarity. In the front view of FIG. 8b , the yand z axes lie in the plane of the paper, while the x axis points out ofthe paper. FIGS. 9a and 9b show the effect of rotating theretroreflector about the −y axis by the pitch angle P, which is 15degrees in this example. This rotation operation results in newcoordinate system: x′, y′, z′, with y=y′. FIGS. 10a and 10b show theeffect of rotating the retroreflector about the z′ axis by the yaw angleY, which is 10 degrees in this example. This rotation results in a newcoordinate system: x″, y″, z″, with z″=z′. FIGS. 11a and 11b show theeffect of rotating the retroreflector about the x″ axis by the rollangle R, which is 40 degrees in this example. Note that in FIG. 11b ,the x axis (direction opposite that of the laser beam) still pointsstraight out of the paper. The roll, yaw, and pitch angles are foundfrom a measurement of the three lines of intersection by the orientationcamera 210. The camera detects the three lines of intersection ofcube-corner retroreflector 107. The vertex of cube-corner retroreflector107, which is defined as the common point of the three reflectingsurfaces, remains centered on the photosensitive array 725 of FIG. 7.The electrical signals from photosensitive array 725 may be sent to alocal digital-signal processing chip or sent over electrical wires 41 toelectronics box 140 of FIG. 1. These electrical components determine theslopes of the three lines of intersection. By definition, the y and zaxes on the surface of photosensitive array 725 point in the horizontaland vertical directions, respectively. The slope of the first(reference) line of intersection is defined as m₁=Δz₁/Δy₁, where Δy₁ andΔz₁ are the horizontal and vertical distances on the surface ofphotosensitive array 725 from the image of the cube-corner vertex to theimage of an arbitrary point on the first line of intersection The slopesof the second and third lines of intersection are defined in a similarmanner as m₂=Δz₂/Δy₂ and m₃=Δz₃/Δy₃. The three unknown angles, the rollangle R, the yaw angle Y, and the pitch angle P, are found bysimultaneously solving the following three equations:

$\begin{matrix}{{m_{1} = \frac{{\sin\; P\;\cos\;{Y/\sqrt{2}}} - {\sin\; P\;\sin\; Y\;\cos\; R} + {\cos\; P\;\sin\; R}}{{\sin\;{Y/\sqrt{2}}} + {\cos\; Y\;\cos\; R}}},} & (2) \\{{m_{2} = \frac{\begin{matrix}{{\sin\; P\;\cos\;{Y/\sqrt{2}}} - {\sin\; P\;\sin\; Y\;\cos\;\left( {R + {120{^\circ}}} \right)} +} \\{{\cos\; P\;{\sin\left( \;{R + {120{^\circ}}} \right)}}\mspace{11mu}}\end{matrix}}{{\sin\;{Y/\sqrt{2}}} + {\cos\; Y\;\cos\;\left( {R + {120{^\circ}}} \right)}}},} & (3) \\{m_{3} = {\frac{\begin{matrix}{{\sin\; P\;\cos\;{Y/\sqrt{2}}} - {\sin\; P\;\sin\; Y\;\cos\;\left( {R + {240{^\circ}}} \right)} +} \\{{\cos\; P\;{\sin\left( \;{R + {240{^\circ}}} \right)}}\mspace{11mu}}\end{matrix}}{{\sin\;{Y/\sqrt{2}}} + {\cos\; Y\;\cos\;\left( {R + {240{^\circ}}} \right)}}.}} & (4)\end{matrix}$For the example considered here in which R is 40 degrees, Y is 10degrees, and P is 15 degrees, Eqs. (2)-(4) yield m₁=0.874, m₂=−0.689,and m₃=−2.651. As a check of these results, the slope values can also becalculated directly from the y and z values of the lines of FIG. 11b .These calculations yield m₁=0.7667/0.8772=0.874,m₂=0.5528/−0.8026=−0.689, and m₃=−0.7788/0.2938=−2.651, which matchexactly the results obtained from Eqs. (2)-(4).

The visibility of the lines on photosensitive array 725 of FIG. 7 may beimproved by increasing the thickness of the lines of intersection ofretroreflector 107 or by coating the lines with a non-reflectivematerial. Thicker lines of intersection on retroreflector 107 will causethe images of the lines seen on the photosensitive array to have highercontrast. However, thicker lines of intersection on retroreflector 107will not usually result in thicker image lines on photosensitive array725. Usually, the thickness of the lines as seen on photosensitive array725 is determined by the effects of diffraction of the laser light thatpasses through the clear aperture of laser tracker 100. The larger theclear aperture (the opening through which the light passes into thetracker), the smaller will be the deleterious effects of diffraction,which included broadening, smearing, and chopping of the image onphotosensitive array 725. The deleterious effects of diffraction arealso smaller when the retroreflector 107 is moved closer to the lasertracker 100. Fortunately, for the system considered here, the smearingeffects of diffraction are symmetrical about the lines of intersection,so there is no bias in measuring the slopes of the lines.

The appearance of the lines on the image of photosensitive array isshown in FIG. 12. The lines on this image that pass through vertex Vappear on both sides of the vertex. By comparison, FIG. 11b shows thatthe lines of intersection of the physical cube-corner retroreflectorappear on only one side of the vertex. This difference is the result ofthe symmetry in the paths that light can take when the laser beam iscentered on vertex V. For example, if a pencil of light reflects offmirror 1, then mirror 2, then mirror 3 of the cube corner, then anotherpencil of light can reflect off mirror 3, then mirror 2, then mirror 1.If, instead of striking a mirror, the pencil of light strikes a line ofintersection, then the light will not reflect back to the tracker and adark spot will appear on the image of photosensitive array 725. However,this dark spot would also appear if the light had traveled in thereverse direction before encountering the line of intersection. Hencelight entering on either side of vertex V is blocked. It is impossibleto tell from the image of the photosensitive array 725 alone which ofthe three line segments corresponds to which of the three lines ofintersection of a cube-corner retroreflector. There are several waysaround this problem. The simplest, but least convenient, method forassigning the lines of the image (FIG. 12) to the lines of intersection(FIG. 11b ) is to have the operator indicate the approximate orientationof probe assembly 180 at the start of a measurement sequence. Anapproximate orientation is sufficient to determine which of the imageline segments corresponds to each of the lines of intersection. Anothersimple but effective method is to temporarily turn off or reduce thepower of the laser beam 153 emitted by laser tracker 100 and, at thesame time, to increase the exposure time of photosensitive array 725.Under these conditions, the photosensitive array will ordinarily be ableto make out the features of housing 109 and hence obtain information onthe orientation of retroreflector 107. A third method for assigning theline segments to the corresponding lines of intersection is described ina second embodiment that is discussed later.

The method for determining the pitch, roll, and yaw angles as describedabove provides has two main advantages. First, an essentiallyconstant-magnification camera maintains the accuracy of the measurementfor a probe located either near the tracker or far from it. Second,elimination of spurious diffraction effects improves accuracy, which mayotherwise change the angles of the lines or dramatically change theappearance of the lines, especially at large distances.

FIG. 1 shows that housing 109 can be pivoted about axis 182 mounted onadjustable stage 181 and then locked in place. This allows cube-cornerretroreflector 107 to be oriented in any desired direction. Thisflexibility in the orientation of retroreflector 107 is desirablebecause it allows probe tip 171 to be placed in slots, holes, and soforth at any given angle. Preferably shaft 182 is aligned with thevertex of retroreflector 107 to simplify calculations to determine thelocation of probe tip 171. If the locking mechanism allows a limitednumber of angular adjustments, each known to a sufficient angularaccuracy (perhaps a few arc seconds), then measurement may resume assoon as the lock down is complete. If the locking mechanism is notsufficiently precise, then an alternative approach involves adjustinghousing 109 to any given orientation and performing a simplecompensation routine to determine the angle between retroreflector 107and probe shaft 170. Such a compensation routine might include measuringthe location of a reference point with a spherically mountedretroreflector target and then measuring the same location with probeassembly 180 tilted to cover a range of pitch, yaw, and roll angles.

It is possible to replace the described cube-corner retroreflector 107,which is made of three reflecting mirrors, with a cube-cornerretroreflector prism formed of solid glass. Each type of retroreflectorhas advantages. For example, the cube-corner retroreflector that usesmirrors (also known as a hollow-core cube-corner retroreflector) is moreaccurate because it is not prone to transverse and radial offset errorsand because it has no glass/air interface to cause unwanted opticalreflections. The solid glass cube-corner retroreflector has a widerfield of view and is usually less expensive. Equations (2), (3), and (4)can be readily modified to account for a solid-glass, rather than ahollow-core, cube-corner retroreflector.

Locator-Camera Block

The locator-camera block 230 of FIG. 2 allows laser tracker 100 toquickly determine the approximate location of multiple retroreflectorswithin a wide field of view. The locator camera is shown in greaterdetail in FIGS. 14a and 14b . As shown in FIG. 2, locator-camera block230 is placed to one side of rigid structure 190 and has an aperture at231, which might be considered the “top” side of rigid structure 190.When rigid structure 190 is rotated about the center of shaft 270,locator-camera block 230 faces the retroreflectors in the region ofinterest. Locator-camera block 230 then emits cone of light 1320 asshown in FIG. 13. This light reflects off retroreflectors 107, 1311,1312, and 1313 shown in FIG. 13. Here, retroreflector 107 represents atarget of interest and retroreflectors 1311, 1312, and 1313 represent anumber of other targets. The corresponding reflected light bundles 1357,1351, 1352, and 1353 enter rigid structure 190. The light enteringlocator-camera block 230 falls onto a photosensitive array 1404 in FIG.14b , and the pattern is analyzed to determine the approximate locationof the targets in the region of interest.

FIGS. 14a and 14b depict an example locator-camera arrangement. Aplurality of identical light sources 1401 is provided in a ringsurrounding a lens 1402. The individual light sources emit overlappingcones of essentially incoherent light 1440 that collectively constitutethe cone of light 1320 in FIG. 13. Each of the retroreflectors 107,1311-1313 reflects some of the light from the cone of light 1320 back tothe locator-camera block 230 as the bundles of light 1351-1353 or 1357.The bundle of light 1357 is shown in FIG. 14b . Lens 1402 focuses thebundle 1357 down to a spot on the surface of photosensitive array 1404.The photosensitive array 1404 is separated from the front principalplane, 1403, of lens 1402 by the focal length f of the lens.

Electrical wires 41 provide power from electronics box 140 to lightemitters 1401 and photosensitive array 1404. Electrical wires 41 alsotransmit the pixel data from photosensitive array 1404 to electronicsbox 140 for analysis. Electronics box 41 analyzes the pattern of lighton photosensitive array 1404 to determine the location of central point1452 on photosensitive array 1404. Electronics box 140 also performsthis analysis of the pattern formed by the other bundles of lightreturned by the retroreflectors. In other words, reflected light bundles1357, 1351, 1352, and 1353 are focused by lens 1402 into patterns onphotosensitive array 1404. Electronics box analyzes these patterns todetermine the central point of each pattern. From the location of thecentral points, the approximate angular direction to each of theretroreflectors can be determined.

Suppose that the retroreflector of interest is retroreflector 107. Oncethe information from the locator camera has been used to determine theapproximate direction to retroreflector 107, motors 80 and 81 areactivated to turn rigid structure 190 until laser beam 153 points in theapproximate direction of retroreflector 107. The tracker then begins asearch pattern, in which the direction of laser beam 153 is changed in asystematic fashion. For example, the laser beam might be steered along aspiral pattern. When the laser beam intersects the target, positiondetector 341 of FIG. 3 senses the reflected light. The signals fromposition detector 341 provide enough information to enable motors 80 and81 to point rigid structure 190 directly to the center of retroreflector107.

FIG. 15a shows rays of light emitted by light emitter 1401 located abovelens 1402. Ray of light 1520 travels to vertex V of retroreflector 107.Reflected light 1521 is sent directly back to light emitter 1401. Itdoes not enter lens 1402 or appear as a spot of light on photosensitivearray 1404. Ray of light 1530 is sent to the bottom of retroreflector107 and emerges as reflected light 1532. It also misses lens 1402 andphotosensitive array 1404.

FIG. 15b shows additional rays of light from light emitter 1401 locatedabove lens 1402. Light emitter 1401 sends ray of light 1540 to alocation above vertex V on retroreflector 107. This ray emerges asreflected ray 1541, which passes near the top of lens 1402, is bent intoray 1542, and arrives at photosensitive array 1404 near central point1563. Light emitter 1401 sends ray of light 1550 to the top ofretroreflector 107. This ray emerges as reflected ray 1552, whichtravels to lens 1402, is bent into ray 1553, and arrives atphotosensitive array 1404 near central point 1563. As the distance fromlight emitter 1401 to retroreflector 107 increases, rays 1541 and 1552become nearly parallel, and the spot of light about point 1563 getssmaller and smaller.

FIG. 15c shows rays of light from light emitter 1401 located below lens1402. The rays of light in the bottom diagram are mirror images of therays in the middle diagram. If N is the number of pixels inphotosensitive array 1404, W is the width of photosensitive array 1404,D is the diameter of lens 1402, and h is the distance from the edge oflens 1402 to light emitters 1401, the number of pixels between centralpoints 1563 and 1593 will, in most cases, be less than [2N(D+h)/L]arctan(W/2f). For example, if N=5 12, D=25 mm, h=5 mm, L=3 m, W=13 mm,and f=10 mm, the number of pixels between central points 1563 and 1593will be less than six. Since light emitters 1401 are arranged in acircle, the image will be symmetrical, somewhat blurry, and about sixpixels across. For retroreflectors further than 3 meters away, as mostwill be, the pattern of dots will be smaller. Electrical signals aresent from photosensitive array 1404 through electrical wire 41 toelectronics box 140. Electronics box 140 analyzes the intensity of lightin the pixels to obtain the best estimate of the center of the patternproduced by each retroreflector.

Routing of Optical Fibers

FIG. 16 shows a configuration of a fiber launch laser tracker 1600 forproviding advantageous routing of optical fibers. Here, optical fibersare preferably routed close to the two mechanical axes 1670 and 1671.The routing of the optical fibers in the system of FIG. 16 has manyadvantages. For example, a large angular field of view of the trackercan be obtained. Also, bending or kinking of the optical fibers isprevented, thereby preserving measurement accuracy. Laser beam 1653,which is launched from rigid plate 1690, travels to retroreflector 107as shown in FIG. 1 and returns as laser beam 1663. Laser light fromoptical fiber 1611 is collimated by lens 1613, reflected by mirror 1615,and transmitted through beam splitter 1614. Laser light from opticalfiber 1612 is collimated by lens 1612 and reflected off beam splitter1614. Any number of laser beams can be combined into a common path toform outgoing laser beam 1653. Returning laser light may pass through anumber of elements as previously discussed and omitted in FIG. 16 forclarity. For example, beam splitters for the position detector and theorientation camera may be employed in accordance with the specificapplication. The returning laser light may reflect off beam splitter1614 and pass through lens 1612 to be coupled into optical fiber 1610.Alternatively, the laser light may pass into another device located onrigid plate 1690 for processing as previously discussed, for example,with reference to the absolute distance meter and the interferometer.Similarly, the returning laser light may reflect off mirror 1615 andcouple back into optical fiber 1611. Alternatively, this laser light maytravel to another device on rigid plate 1690 for processing.

The direction of laser beam 1653 is determined by the orientation ofrigid plate 1690, which in turn is determined by the angle of rotationof the zenith mechanical axis 1671 and the azimuth mechanical axis 1670.The zenith motor 1681 rotates the zenith axis 1671, and the azimuthmotor 1680 rotates the azimuth axis 1670. Zenith angular encoder 1691and the azimuth angular encoder 1690 measure the zenith and azimuthangles. Bearings 1681 and 1680 are also attached to the zenith andazimuth axes. The outside of zenith bearings 1621, zenith angularencoder 1691, and zenith motor 1681 are attached to the azimuthstructural frame (not shown). The azimuth structural frame turns withthe azimuth axis. Consequently, the zenith axis rotates within theazimuth structural frame. The outside of azimuth bearings 1620, azimuthangular encoder 1690, and azimuth motor 1680 are attached to stationarystructural frame (not shown). The stationary structural frame isstationary with respect to the surroundings to which the tracker ismounted. Consequently, the azimuth axis rotates within the stationarystructural frame.

Optical fibers 1610 and 1611 are incorporated into optical fiberassembly 1605. Optical fiber assembly 1605 passes through zenith axis1671 and azimuth axis 1670. Lasers within optoelectronic module 1606(which, like the azimuth motor 1680, is stationary) inject laser lightinto optical fibers 1610 and 1611. Optoelectronic module 1606 may alsocontain optical detectors and electronics to determine the distance toretroreflector 107 or to a diffuse surface under investigation. Theoptical fiber assembly 1605 travels from optoelectronic module 1606 tothe underside of azimuth axis 1670. It is attached to the stationarystructural frame near point A shown in FIG. 16. At point A, the fiber isstationary with respect to the rotating azimuth axis. At the other endof the azimuth axis, optical fiber assembly 1605 is attached to theazimuth structural frame near point B, which rotates along with azimuthaxis 1670. Since one end of the fiber is fixed and the other end of thefiber is rotating with respect to the rotation of the azimuth axis, theoptical fiber will experience a torsional twist. In most cases, a gentletwist of this sort will not degrade measurement accuracy. Optical fiberassembly 1605 is routed to the zenith axis, where it is attached to theazimuth structural frame near point C. At point C, the fiber isstationary with respect to the rotating zenith axis. At the other end ofthe zenith axis, fiber assembly 1605 is attached near point D, whichrotates along with the zenith axis 1671.

Optical fiber assembly 1605 is routed through the two mechanical axes.The fiber assembly is stationary at one end of each axis. At the otherend, the fiber assembly rotates along with the axis. This produces atorsional twist, which is acceptable in most situations. A slightlydifferent method of routing optical fiber assembly 1605 near the twomechanical axes may be preferable in some cases. In this method, theoptical fibers are placed in coils to the outside of the mechanicalaxes, with the end of the optical fiber attached at one end to a pointthat is stationary relative to the mechanical axis and at the other endattached to a point that moves with the mechanical axis. Here, thediameter of the coils will change slightly as the axis is rotated. Inmost cases, this small change in the radius of the coiled fiber assemblywill not adversely affect measurement accuracy. By heat treating fiberassemblies, it is possible to make low-cost cables that naturally coilinto the desired geometry, thereby simplifying production and increasingreliability.

Second Embodiment

The second embodiment of the invention is generally similar to thatshown in FIG. 1 except for the probe assembly 180 is replaced by probeassembly 1780, as shown in FIG. 17. Probe assembly 1780 contains asingle small retroreflector 1708 to the side of retroreflector 107.Retroreflector 1708 is approximately aligned with the first line ofintersection. At the start of the measurement, the photosensitive array725 of FIG. 7 displays a pattern similar to that of FIG. 12, with thedetails of the pattern dependant on the pitch, yaw, and roll angles ofretroreflector 107. As explained previously, at the start of themeasurement, it is not possible to tell which line segments correspondto each of the three lines of intersection. To resolve this ambiguity,the tracker performs a search in which it directs laser beam 153 insuccession to each of the six possible locations of retroreflector 1708.A flash of light on position detector 341 of FIG. 3 indicates that thefirst line of intersection has been identified. Also on probe assembly1780, two thin wires 1711 and 1712 have been stretched across the top ofretroreflector 107. Additional thin wires or alternative shapes may alsobe used. These wires provide redundant information for determining thepitch, yaw, and roll angles for those cases in which accuracy is moreimportant than measurement speed.

Probe assemblies 180 and 1780 can be used in either a scanning mode or atrigger mode. In the scanning mode, probe tip 171, shown in FIGS. 1 and17, is moved across the surface of the object under evaluation 175 whiledata is continually collected at a high rate. In the trigger mode, probe180 or 1780 is moved successively to the points of interest. When theprobe is properly positioned, the operator triggers the measurement byperforming an action such as pressing a button or issuing a voicecommand.

Either target object 185 in the first preferred embodiment or targetobject 1785 in the second preferred embodiment can be detached fromadjustable stage 181 and probe shaft 170, then attached to the endeffector of a robot arm. Alternatively, the target object can beattached to a machine tool such as a drilling or milling machine. Thetracker sends a laser beam to the target object to determine the sixdegrees of freedom of the drill or mill. The information provided by thetracker on the six degrees of freedom of target object 185 or 1785 canbe used in a control loop to precisely direct the machine tool or robotend effector to the desired locations. If the tracker measures the sixdegrees of freedom fast enough, real-time control of machine tools androbots is possible.

Third Embodiment

The third embodiment of the invention provides a laser tracker 1800 asshown in FIG. 18 that uses a steering reflector 1804 within gimbal mount95 to direct laser beam 1853 to retroreflector 107. Laser 1802 emitslaser light that is sent to retroreflector 107. Optical block 1806contains beam expander 220 and any other optical beam-conditioningelements that may be required. Laser light returning from retroreflector107 is sent to distance-measuring device 1814, which may be either anabsolute-distance meter or an incremental-distance meter. Part of thereturning laser light is also reflected off beam splitter 1809 toposition detector 341. The beam splitter 701 reflects a portion of laserbeam 54 into orientation-camera subsystem 1810. Orientation camerasubsystem 1810 comprises afocal lens block 710 and relay/array block720, also shown in FIG. 7. The optical elements within blocks 1806 and1810 of FIG. 18 are substantially equivalent to the optical elementswithin blocks 220 and 210 of FIGS. 6 and 7. In effect, an orientationcamera comprising elements 701 and 1810 is embedded within laser tracker1800. This orientation camera is equivalent to the orientation camera210 of FIG. 2 and can therefore be used to measure the six degrees offreedom of target object 185.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the laser-based coordinatemeasuring device of the present invention without departing from thespirit or scope of the invention. Thus, it is intended that the presentinvention covers the modifications and variations of this inventionprovided they come within the scope of the appended claims and theirequivalents.

What is claimed is:
 1. A method of steering a first laser beam from aninstrument toward a first point on a first retroreflector, the methodcomprising: providing the first retroreflector; providing athree-dimensional (3D) measurement instrument having a first axis, asecond axis, a first plane, a second plane, a first angle transducer, asecond angle transducer, a position detector, a distance meter, and afirst camera, the first camera including a first lens and a firstphotosensitive array, the first axis and the second axis substantiallyintersecting at a gimbal point, the first plane including the first axisand is perpendicular to the second axis, the second plane including thesecond axis, the first plane and the second plane intersecting in afirst line, the instrument operable to rotate the first plane about thefirst axis and the second plane about the second axis, the positiondetector operable to intercept light reflected by the firstretroreflector and to indicate a position of the intercepted light onthe position detector, the distance meter operable to measure a distancefrom the gimbal point to the first point; emitting from the instrument acone of light along a third optical axis, the third optical axisoperable to rotate about the first axis; intercepting with the firstretroreflector a first part of the cone of light to form a first regionof light at the first retroreflector; intercepting with the first lens afirst portion of the cone of light reflected by the firstretroreflector; acquiring with the first photosensitive array a firstimage that includes an image of the first region; determining a firstposition on the first photosensitive array of the image of the firstregion; determining a first angular increment of the first plane and asecond angular increment of the second plane based at least in part onthe first image, wherein the first angular increment and the secondangular increment are calculated to steer the first laser beam to thefirst point based at least in part on the determination of the firstposition; rotating the first plane to a third angle to produce the firstangular increment of the first plane and rotating the second plane to afourth angle to produce the second angular increment of the secondplane; intercepting with the position detector a second portion of thefirst laser beam reflected by the first retroreflector; rotating thefirst plane to a fifth angle and rotating the second plane to a sixthangle, the fifth angle and the sixth angle calculated to place thesecond portion at a predetermined location on the position detector;measuring the fifth angle of rotation with the first angle transducerand measuring the sixth angle of rotation with the second angletransducer; measuring a first distance with the distance meter; anddetermining three-dimensional coordinates of the first point based atleast in part on the fifth angle, the sixth angle, and the firstdistance.
 2. The method of claim 1, further including a step ofadjusting the first plane and second plane during movement of the firstretroreflector to keep the second portion directed to the predeterminedlocation on the position detector.
 3. The method of claim 1, wherein thestep of rotating the first plane to a third angle and rotating thesecond plane to a fourth angle to further includes steps of: steeringthe first laser beam in a first pattern in space; monitoring whether thesecond portion of the first laser beam reflected by the firstretroreflector has been received by the position detector; and stoppingthe steering of the first laser beam in the first pattern in response tothe second portion being on the position detector.
 4. The method ofclaim 3, wherein the step of rotating the first plane to a fifth angleand rotating the second plane to a sixth angle further includes a stepof adjusting the first plane and second plane during movement of thefirst retroreflector to keep the second portion directed to thepredetermined location on the position detector.
 5. The method of claim1, wherein, in the step of sending a cone of light, the direction of thecone of light is determined at least in part by the third angle.
 6. Themethod of claim 1, wherein: the step of providing the firstretroreflector further includes a step of providing a secondretroreflector, the second retroreflector having a second point;intercepting with the second retroreflector a second part of the cone oflight to form a second region of light at the second retroreflector; thestep of intercepting with the first lens a first portion of the cone oflight reflected by the first retroreflector further includes a step ofintercepting with the first lens a third portion of the cone of light,the third portion reflected by the second retroreflector; in the step ofobtaining a first image on the first photosensitive array, the firstimage further includes an image of the second region; and the step ofdetermining a first position further includes a step of determining andstoring a second position, the second position being a position on thefirst photosensitive array of the image of the second region.
 7. Themethod of claim 6, further including steps of: calculating a thirdangular increment of the first plane and a fourth angular increment ofthe second plane, wherein the third angular increment and the fourthangular increment are calculated to steer the first laser beam to thesecond point; rotating the first plane to a seventh angle to produce thethird angular increment and rotating the second plane to an eighth angleto produce the fourth angular increment; intercepting with the positiondetector a fourth portion of the first laser beam reflected by thesecond retroreflector; rotating the first plane to a ninth angle androtating the second plane to a tenth angle, the ninth angle and thetenth angle calculated to place the fourth portion at the predeterminedlocation on the position detector; measuring the ninth angle of rotationwith the first angle transducer and measuring the tenth angle ofrotation with the second angle transducer; measuring a second distancewith the distance meter; and determining three-dimensional coordinatesof the second point based at least in part on the ninth angle, the tenthangle, and the second distance.
 8. The method of claim 1, wherein thepredetermined position is located at the center of the positiondetector.
 9. A system of steering a first laser beam, the systemcomprising: a first retroreflector; a 3D measurement instrument having afirst axis, a second axis, a first plane, a second plane, a first angletransducer, a second angle transducer, a position detector, a distancemeter, an electronics circuit and a first camera, the first cameraincluding a first lens and a first photosensitive array, the first axisand the second axis substantially intersecting at a gimbal point, thefirst plane including the first axis and is perpendicular to the secondaxis, the second plane including the second axis, the first plane andthe second plane intersecting in a first line, the instrument operableto rotate the first plane about the first axis and the second planeabout the second axis, the position detector operable to intercept lightreflected by the first retroreflector and to indicate a position of theintercepted light on the position detector, the distance meter operableto measure a distance from the gimbal point to the first point; acomputer operably coupled to the 3D measurement instrument, the computercooperating with the electronics circuit to perform a method comprising:emitting from the 3D measurement instrument a cone of light along athird optical axis, the third optical axis operable to rotate about thefirst axis; intercepting with the first retroreflector a first part ofthe cone of light to form a first region of light at the firstretroreflector; intercepting with the first lens a first portion of thecone of light reflected by the first retroreflector; acquiring with thefirst photosensitive array a first image that includes an image of thefirst region; determining a first position on the first photosensitivearray of the image of the first region; determining a first angularincrement of the first plane and a second angular increment of thesecond plane based at least in part on the first image, wherein thefirst angular increment and the second angular increment are calculatedto steer the first laser beam to the first point based at least in parton the determination of the first position; rotating the first plane toa third angle to produce the first angular increment of the first planeand rotating the second plane to a fourth angle to produce the secondangular increment of the second plane; intercepting with the positiondetector a second portion of the first laser beam reflected by the firstretroreflector; rotating the first plane to a fifth angle and rotatingthe second plane to a sixth angle, the fifth angle and the sixth anglecalculated to place the second portion at a predetermined location onthe position detector; measuring the fifth angle of rotation with thefirst angle transducer and measuring the sixth angle of rotation withthe second angle transducer; measuring a first distance with thedistance meter; and determining three-dimensional coordinates of thefirst point based at least in part on the fifth angle, the sixth angle,and the first distance.
 10. The system of claim 9, wherein the methodfurther includes a step of adjusting the first plane and second planeduring movement of the first retroreflector to keep the second portiondirected to the predetermined location on the position detector.
 11. Thesystem of claim 9, wherein the step of rotating the first plane to athird angle and rotating the second plane to a fourth angle to furtherincludes steps of: steering the first laser beam in a first pattern inspace; monitoring whether the second portion of the first laser beamreflected by the first retroreflector has been received by the positiondetector; and stopping the steering of the first laser beam in the firstpattern in response to the second portion being on the positiondetector.
 12. The system of claim 11, wherein the step of rotating thefirst plane to a fifth angle and rotating the second plane to a sixthangle further includes a step of adjusting the first plane and secondplane during movement of the first retroreflector to keep the secondportion directed to the predetermined location on the position detector.13. The system of claim 9, wherein, in the step of sending a cone oflight, the direction of the cone of light is determined at least in partby the third angle.
 14. The system of claim 9, wherein: the step ofproviding the first retroreflector further includes a step of providinga second retroreflector, the second retroreflector having a secondpoint; intercepting with the second retroreflector a second part of thecone of light to form a second region of light at the secondretroreflector; the step of intercepting with the first lens a firstportion of the cone of light reflected by the first retroreflectorfurther includes a step of intercepting with the first lens a thirdportion of the cone of light, the third portion reflected by the secondretroreflector; in the step of obtaining a first image on the firstphotosensitive array, the first image further includes an image of thesecond region; and the step of determining a first position furtherincludes a step of determining and storing a second position, the secondposition being a position on the first photosensitive array of the imageof the second region.
 15. The system of claim 14, wherein the methodfurther including steps of: calculating a third angular increment of thefirst plane and a fourth angular increment of the second plane, whereinthe third angular increment and the fourth angular increment arecalculated to steer the first laser beam to the second point; rotatingthe first plane to a seventh angle to produce the third angularincrement and rotating the second plane to an eighth angle to producethe fourth angular increment; intercepting with the position detector afourth portion of the first laser beam reflected by the secondretroreflector; rotating the first plane to a ninth angle and rotatingthe second plane to a tenth angle, the ninth angle and the tenth anglecalculated to place the fourth portion at the predetermined location onthe position detector; measuring the ninth angle of rotation with thefirst angle transducer and measuring the tenth angle of rotation withthe second angle transducer; measuring a second distance with thedistance meter; and determining three-dimensional coordinates of thesecond point based at least in part on the ninth angle, the tenth angle,and the second distance.
 16. The system of claim 9, wherein thepredetermined position is located at the center of the positiondetector.